×

zbMATH — the first resource for mathematics

Robust stabilization of uncertain linear dynamical systems. (English) Zbl 0781.93074
Summary: Based on the stabilizability of a nominal system (i.e. a system in the absence of uncertainty), by making use of the Lyapunov stability criterion and combining with the algebraic Riccati equation, a new approach for designing a robust linear state feedback controller for uncertain linear dynamical systems is presented. Using this approach, the BIBO stability of uncertain linear dynamical systems is also discussed. Some analytical methods and the Bellman-Gronwall inequality are employed to investigate the robust stabilization conditions on the feedback controller. The main features of this approach are that no matching condition about uncertainty is needed and the uncertain systems can be asymptotically stabilized. An example is given to demonstrate the validity of our results.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C05 Linear systems in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1137/0321014 · Zbl 0503.93049
[2] DOI: 10.1109/TAC.1982.1102862 · Zbl 0469.93043
[3] DOI: 10.1080/00207178208922617 · Zbl 0489.93041
[4] DOI: 10.1080/00207178608933559 · Zbl 0606.93028
[5] DOI: 10.1080/00207178708933831 · Zbl 0623.93023
[6] DOI: 10.1109/TAC.1981.1102785 · Zbl 0473.93056
[7] DOI: 10.1109/TAC.1976.1101137 · Zbl 0326.93007
[8] DOI: 10.1109/TAC.1980.1102374 · Zbl 0442.93024
[9] Franklin J. N., Matrix Theory (1968) · Zbl 0174.31501
[10] DOI: 10.1109/TAC.1979.1102073 · Zbl 0416.93076
[11] DOI: 10.1137/0320060 · Zbl 0504.49024
[12] DOI: 10.1115/1.3426427 · Zbl 0416.93077
[13] DOI: 10.1080/00207177708922217 · Zbl 0343.93062
[14] Patel R. V., Proc. Joint Automtic Control Conf. (1988)
[15] DOI: 10.1109/TAC.1977.1101658 · Zbl 0368.93028
[16] DOI: 10.1007/BF00934932 · Zbl 0446.93040
[17] DOI: 10.1109/TAC.1982.1103015 · Zbl 0486.93051
[18] DOI: 10.1109/TAC.1981.1102603 · Zbl 0474.93025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.